| Eugene Lashchyk, Scientific Revolutions, 1969 |
Chapter III
Toward a Rational Reconstruction of SSR
In the previous chapter I have tried to show, among other things, that there are many senses of the term "paradigm" in SSR. Because of such a plurality of meanings some readers mistakenly have taken one of these meanings of the term "paradigm" as central to all the uses of the term.{1} Also, as I have suggested in the previous chapter, Kuhn is interpreted as being inconsistent on the question of scientific change by Mary Hesse and Israel Scheffler, in part due to such homonymous use of the term "paradigm". In order to circumvent such misinterpretations of Kuhn's ideas, as well as some possibly unintentional exaggerations by Kuhn himself as in the case of T3, I propose to turn in this chapter to a more constructive part namely, the rational reconstruction of the technical machinery of Kuhn's book The Structure of Scientific Revolutions. By a rational reconstruction I have in mind a reconstruction that fulfills the following requirements: a) it is in the spirit of the basic ideas of the work; b) it is presented in terms that are clear and when possible more precise than the original; c) the reconstruction must at least meet the most basic requirement of rationality, namely, consistency.{2} To get at the spirit of SSR. I think it best that we look at the problems that confronted Professor Kuhn and which motivated him to introduce the controversial term "paradigm" in terms of which he attempted to solve these problems.{3} 1. Being not only a physicist by training but also a historian of science by profession, Professor Kuhn was struck by the fact that not only at present but also during certain periods in the past history of science there existed well defined scientific communities each with their own peer group. The problem was to explain what held such communities together particularly during those times when there was no fully developed scientific theory. Not only are there times when there is no developed theory, but even when the theory is available there is no body of rules directing the scientific activity.{4} In the absence of a detailed set of rules or recipes, how is it possible for scientists to practice science, i.e.: a) solve problems, b) perform experiments; c) pass judgements on the admissibility of different kinds of evidence; d) decide which problems are scientific rather pseudo-scientific? Let me call this the paradox of a coherent scientific tradition. 2. Most of the technical terms employed by a scientist are not defined exactly. By an exact definition of a word "x" I mean a definition which lists those characteristics that are necessary and sufficient for the application of the word "x". In the absence of exact definitions for most of the terms employed by scientists, how is communication possible within a scientific community? Let me call this the paradox of communication. Further clarification is here needed because this paradox should not be confused with Scheffler's paradox of a common language,{5} which concerns the problem of communication between scientists in different scientific communities or scientists who are committed to different basic theories. The paradox of communication is the more basic of the two for it seems to deny the possibility of communication within presumably coherent scientific groups. Professor Kuhn resolved the above paradoxes plus many other problems of a fundamental nature by appealing to the existence of paradigms. In resolving what I have called the paradox of a coherent scientific tradition, Kuhn's answer in SSR is that commitment to the same paradigm enabled the scientific community to function as a group. He states: By choosing it [the term "paradigm"] I mean to suggest that some accepted examples of actual scientific practice -- examples which include law, theory, application, and instrumentation together -- provide models from which spring particular coherent traditions of scientific research.{6}The paradigm provided scientists with examples of acceptable solutions to problems. It is the paradigm which enables scientists to decide which evidence is admissible and which is to be ruled as unacceptable. It was the phlogiston paradigm which placed high value on explanations in terms of qualitative terms. It enabled phlogistonians to posit negative weight for phlogiston when there was no other way to explain the loss of weight in chemical reactions which presumably involved a combination of phlogiston with some other chemicals. It was the oxygen paradigm of Lavoisier which determined quantitative measurement of weight of all ingredients before and after the chemical reactions to be of paramount importance. It was Maxwell's electromagnetic paradigm which enabled scientists to pass judgment that to search for the effects of the "ether wind" is no longer a scientific problem, but one that is to be relegated to the class of pseudo-scientific problems. In answer to the difficult problems of the demarcation between science and metaphysics the answer in SSR appears to be extreme]y obvious.{7} If a field has a universally accepted paradigm then ipso facts it becomes a science.{8} Basically the motto seems to be "No science, no paradigm."
In a similar fashion one can already see an answer to the paradox of communication. It should be pointed out that this paradox is not explicitly identified as such in SSR. I believe, however, that it is implicit in Kuhn's reference to Wittgenstein's notion of family resemblances and his introduction of the term paradigm for this sense. Kuhn also believes that most terms in a scientist's vocabulary are not defined and yet somehow scientists can get by in their conversations with other scientists in the same community. Communication becomes possible because scientists are acquainted with the same paradigm. The paradigm somehow supplies scientists with examples for the terms employed in their laws and theories. In discussing the reasons for introducing "paradigms" into talk about science, Kuhn states:
Close historical investigation of a given specialty at a given time discloses a set of recurrent and quasi-standard illustrations of various theories in their conceptual, observational, and institutional applications. These are the community's paradigms, revealed in its textbooks, lectures, and laboratory exercises. By studying them and by practicing with them, the members of the corresponding community learn their trade.{9}Because scientists study in their textbook basically the same illustrations of scientific terms which appear in laws and theories, communication is possible.
In Chapter I, I tried to show that there are at least five different senses of the term "paradigm". In Chapter II it appears that answers to the basic question of SSR are also all couched in terms of the same term. Paradigm is an umbrella term which covers many senses among them the following a) theories of limited scope; b) theories of universal scope -- basic theories; c) achievements recounted in textbooks; d) universally recognized scientific achievements; e) a tool capable of solving problems it defines; f) supplies scientists with a view of the constitution of nature and the world; g) supplies scientists with standards which distinguish a real scientific solution from a metaphysical one; h) a clear illustration of the application of key terms employed in laws and theories; i) model.{10} It does not take much wisdom to see that the term is heavily overworked. Why not call each of the many senses of the term "paradigm" in SSR by a term which has already an accepted usage in the scientific and philosophical communities, rather than make one term do so much work and at that, sometimes poorly? A supporter of the status quo concerning the terminology of SSR might say, "Don't touch the book. It is a beautiful masterpiece as it stands. Everything is just right. Just look at the large number of scientists and historians of science that have hailed the work, each saying that Kuhn has magnificently captured exactly what we (scientists) are engaged in." I agree that Kuhn's SSR is one of the best books on the subject of science. I have yet to read a philosophy of science book that was nearly as revealing about science as SSR. Also, I am not doubting that scientists are sincere when they say that SSR has a way of appearing to be just right concealing the description of scientific development and scientific activity. Science is mysterious and Kuhn's use of "paradigm" has succeeded in capturing this mystery, partly by being mysterious itself. This type of argument is heard not only among scientists, but also among philosophers. Many times I have heard statements of the following nature: "Life is mysterious and so must be our philosophy; science is mysterious and so must be our talk about science or our philosophy of science." In each case the conclusion does not follow. I believe that it is one of the main functions of philosophers of science to remove the mystery, to make science and its development transparent. Philosophers must microscopically analyze the ideas of scientists who try to describe their own activity. This is proposed not because scientists don't know what they are talking about, but because scientists don't always put it in a way that meets the rigor of philosophical scrutiny. The quarrel is not so much with what scientists say about science, but more often with how they say it. In this spirit, I approach next the problem of the rational reconstruction of the terminology of SSR. In my revision of the terminology of SSR I would like to select, whenever possible, terms which already have an established usage in scientific and philosophical contexts. The resulting product of such a program will tend to be less original, but hopefully more understandable and clear. Following such a program, I have turned to dictionaries and logic texts and found the following meanings of the term "paradigm":
Dictionary1. Example, pattern; mistake the paradigm for the theory -- Margaret Mead; paradigms of musical perfection H. G. Aiken.
2. An example of a conjugation or declension showing a word in all its inflectional forms, such as amo, amas, amat.
3. A narrative passage in the Gospels that illustrates a saying of Jesus and represents one of the literary patterns distinguished by form criticism; the paradigm . . . is represented in its purity by the healing of the paralytic -- Times Lit. Supp.{11}
Logic Text{12}
4. In logic a paradigm example for a word x is a c]ear-cut case of a thing which is called x.
It is this fourth use of paradigm that turns out to be helpful for our problem. Let us examine what this fourth meaning of "paradigm" is.
Proposal for the Definition of the Term "Paradigm"
We know that every day we succeed in conveying information to others, and yet when we are asked for an exact definition for the terms which we employ we are at a loss most of the time for we don't know the distinguishing or common characteristics which all things such as houses or games have in common. Putting this in a little more technical language, we can say that a definition for a word x is an exact definition if and only ii it gives the conjunction of characteristics each of which is necessary and which together are the sufficient conditions for calling something "x".{13} To provide such a definition for our everyday words is an extremely difficult, if not impossible matter, without becoming arbitrary and dogmatic. But if we are unable to supply exact definitions for everyday words, then this seems to deny the possibility of communication. This result I shall call the paradox of communication. The dilemma is resolved once we realize that even though we are unable to provide exact definitions for terms like "buildings," "tables," etc., we are able to point to certain clear cases of buildings, table, and the like, because we have become acquainted, by convention, with paradigm examples of things denoted by such and such words. In resolving the paradox of communication, we can say that because we all have learned from childhood the same kind of paradigm examples that are denoted by such words as "building," "show," etc., when we speak of buildings, shoes, etc., we mean (denote) the same kind of things. By "meaning" in this context, I mean we are able to point out the same paradigm or clear-cut examples of these words. Our paradigm examples of buildings will have some characteristics in common though not necessarily the same characteristics. The paradigm examples will be related by what Wittgenstein has called the relation of family resemblance.{14} This can best be illustrated by the following example about the characteristics of games. If we let capital letters stand for characteristics of games and each grouping of capital letters to stand for a class of games, then we will see that there is no one characteristic that is held in common by all games (i.e., A,B,C; B,C,D; A,C,D; B,D,E). Such a relationship of partially overlapping characteristics is what Wittgenstein has called the relation of family resemblance. Communication is possible not because everyone in a linguistic community points to the same paradigm, (i.e., everyone would point to the Empire State Building when asked for a clear-cut example of a building) but because the paradigm or clear-cut examples would be of the same kind. Two examples will be said to be of the same kind if their characteristics are connected by the relation of family resemblance, where those characteristics will be taken as representing a family resemblance, which are normally taken as good indications of an item being classified as an x The paradox of communication also arises in scientific communities. How is it possible for scientists in a particular scientific community to understand each other, conduct research, determine acceptable interpretations of concepts, such as metal, insect, oxygen, motion, compound, mixture, in the absence of exact definitions for such words? Part of the answer to the above question lies in the accepted paradigm examples of these terms. What is understood by these terms is contextually given by the sorts of clear-cut examples of these terms which everyone in a particular scientific community comes to understand. We must, however, extend the notion of a paradigm as a clear-cut case of "x" to such things as problem solving situations and laboratory experiments. This extension is obvious, for the training of scientists usually takes place in laboratories where they spend much time preparing and performing experiments. I remember that during my undergraduate days as a science major, the biggest problem with scheduling courses, was finding time for the laboratory sessions, which at times doubled the number of class room hours normally required for liberal arts students. It is during such laboratory sessions that a young science student learns the meaning of scientific terms, not so much by definition as by seeing the "new" terms in concrete experimental application. Kuhn relates an example of a physicist and a chemist who were asked whether or not a single atom of helium was or was not a molecule? Kuhn says: .
Both answered without hesitation, but their answers were not the same. For the chemist the atom of helium was a molecule because it behaved like one with respect to the kinetic theory of gases. For the physicist, one the other hand, the helium atom was not a molecule because it displayed no molecular spectrum. Presumably both men were talking of the same particle, but they were viewing it through their own research training and practice.{15}Besides such sophisticated examples of the meaning of scientific terms, a scientist learns by paradigm example, such terms as microscope, cloud chamber, spectroscope, etc. Related to laboratory experimental situations are the sort of clear-cut examples of the application of certain terms that a science student learns in problem-solving situations. Here the student sees the actual application of such terms as force, mass and acceleration in real problem-solving situations. By the repeated applications of the law, F = MA in problems, the student will come to an understanding of the meaning of these terms. For theoretical terms such as electron, proton, neutron, the physicist must rely almost completely on problem-solving situations and less on laboratory experiments. He cannot avail himself of the rather easy move that the ordinary man has when he is challenged on the meaning of the term "house" or "game". For both there were paradigm or clear-cut examples, except that in the case of a scientist, they take a longer time to acquire.
Let me here inject a comment concerning the very heated debate that is presently raging in the pages of philosophical journals concerning the problem of meaning change. I believe that it is not enough that the same word is employed in theories that it have the same or different meaning. One must look at the illustrations of such terms as force, compound, etc., that are provided by the scientific community in their textbooks and laboratory experiments. These illustrations must be different in kind before one can conclude that they differ in meaning. I do not want to hold the view that because a term a appears in two different theories, let us say theory A and B. that therefore the same term must necessarily differ in meaning. Whether in the transition from theory A to theory B there occurred a change in meaning of the term alpha cannot be determined a priori. Questions of change of meaning must be settled individually by inspection not only of the conceptual relationship of alpha to other concepts but also in the paradigm examples or standard illustrations of the term in each theory. Our reconstruction has so far barely scratched the surface of the rich meaning of paradigm that is found in SSR. Moreover, my present definition of paradigm, as a clear-cut example of the application of some term whether in laboratory experiments or in problem-solving, is incapable of resolving the paradox of a coherent scientific tradition. It is capable however, of resolving the paradox of communication as I have already shown. It can be said that some progress has been made even though I have only redefined, hopefully with some clarity, only a very small portion of the many senses of the term "paradigm." Let me turn next to the paradox of a coherent scientific tradition. Having clear-cut examples of the terns employed in laws and theories is not enough to account for the coherence of a scientific tradition. We must therefore try to make explicit what else must be part of the conceptual framework of a community of scientists that would explain the coherence in such traditions. We no longer have the easy way out that is available in SSR, i. e., that the adoption of the same paradigm explains the coherence in a scientific community. Our narrower conception of paradigm does not ex plain it. Nor is it much more illuminating to say that it is a particular theory of physics or chemistry, etc., which explains the coherence of a scientific tradition. This suggestion would be much more fruitful were it the case that whenever there was a scientific community there was necessarily at the same time a fully developed theory. But such is not the case. One only has to read some of the recent histories of science to notice that more often than not such communities conduct scientific research in the absence of a fully developed theory. One might say that one of the aims of a scientific tradition is to make refinements in the laws and hypotheses deemed important so that the end product might be a fully developed theory. But since such theories are not available for most of the life of a scientific community, appeal to theories to explain the coherence in the tradition is misleading. Philosophers of science as well as some scientists have often equated science with a fully developed theory. To look at science by looking only at the end product of scientific activity provides a distorted view of this activity. One must bring into the picture not only the finished product, but more importantly, one must identify the ingredients of the process that way ultimately responsible for the end product. I think it can he said that this aspect is one of the many positive contributions of Kuhn's approach to the study of science. Ignoring the activity and the concentration on the finished product of science has led to the popular but erroneous view of science. The problem that I am faced with at present is to identify the kinds of components of a conceptual scheme of scientists in a particular scientific specialty at a particular period of normal science that would account for the coherence that seems to characterize a particular scientific community. Coherence in a scientific community is not an all or nothing affair. I believe that coherence is a matter of degree which admits of more or less. Because of this, the degree of coherence present in a particular scientific community will be, in part, a function of the extent of development of the components of their conceptual scheme. Thus, it should not be assumed that just because I have included a component in a conceptual scheme of scientists,in a scientific community, that it necessarily will be fully explicated during any period in the development of that science. I believe however, that with the development of a science more and more of the components will be more fully developed. The development of the parts of a conceptual scheme is in part the work of scientists in a particular period of normal science. I would like to argue that the following are the parts of a conceptual scheme that every scientific community possesses. These parts will appear in varying degrees of development in the history of a scientific specialty. A. There is the Cognitive Matrix{16} which is closely connected with the usual conception of science. Such a cognitive matrix has the following components at various levels of development: (l) Definitions.
(2) Laws; (a) nomological], (b) statistical.
(3) Models; (a) mathematical (b) physical.
(4) Paradigms -- as defined above.
(5) Paragons -- classical papers or textbooks.
(6) Principles and Rules.
(7) Categories.B. Meta-Science. In this group are contained the general ingredients of rational inquiry not peculiar so much to any one specialty of science but rather generally accepted by the whole scientific community irrespective of their specialization. I am interested here in stressing the possible areas of agreement among scientists, rather than concentrating on the differences that might and do exist from field to field. I also believe that the standards in our meta-science are subject to change but they change more slowly. The parts of a cognitive matrix change much more rapidly and at times almost completely. To the area of Meta-Science belong the following considerations:
(2) Deductive Logic.
(3) Mathematical Theories.I would like to make some remarks at present about some of the components of the conceptual scheme. I have included "definitions" as a separate component of the cognitive matrix (C. M.), because of the important role that definitions play in science. Many times scientists introduce a new term by an explicit definition. This need not be an exact definition, one that lists all of the necessary and sufficient characteristics that must be present before an object will be called x. A definition might list only some of those characteristics which a scientist considers to be central. In any case, their role cannot be underestimated.{17} A clear indication of revolutionary change can be had whenever it becomes necessary to change the basic definition of terms employed in laws. Much of the work in recent philosophy of science has centered on the concept of law.{18} Its importance for science is unquestionable. As a matter of fact, the possessing of laws by a discipline might be taken as an important indication that it has achieved the status of a full-fledged science. Furthermore, the fact that models are separately (included in the C. M. has various advantages over just having the term "paradigm" stand for everything including models. I will briefly describe the important role models have played in the development of science and at the same time cite some definitions of models in sentence. The construction of physical models for scientific theories have enabled scientists in the past to get a clearer understanding of the theoretical terms employed in definitions and laws. Besides deepening scientists' understanding of a theory, models have also enabled scientists to extend the field of application of a law to heretofore unsuspected phenomena. Take, for example, water flowing through a pipe as a model for suggesting certain laws pertaining to the movement of traffic, or water waves as suggestions of certain properties of sound waves, in each case models were used as means of discovering laws in other fields.{19} Actually the important element in the comparison of such models is the analogies that obtain between each of the models or between a physical model and certain theoretical terms of laws in another science. Thus, analogies are extremely important in the development not only of one theory, but also as a method of discovery extending areas of application from one discipline to another. Pierre Duhem brilliantly describes such a role of analogies in science. He states:
. . . it may happen that the equations in which one of the theories is formulated are algebraically identical to the equations expressing the other. Then, although these two theories are essentially heterogeneous by the nature of the laws which they coordinate, algebra establishes an exact correspondence between them. Every proposition of one of the theories has its homologue in the other: every problem solved in the first poses and resolves a similar problem in the second. Each of these two theories can serve to illustrate the other, according to the words used by the English: "By physical analogy" Maxwell said, "I mean that partial resemblance between the laws of a science and the laws of another science which makes one of the two sciences serve to illustrate the other." (Maxwell, Scientific Papers l, 156)Further down Duhem states that ". . . this sort of algebraic correspondence between two theories, . . . not only does it bring a notable intellectual economy . . . But it also constitutes a method of discovery."{20} Still another type of model in science is the mathematical model. Patrick Suppes describes it as follows:
Roughly speaking a model of a theory may be defined as a possible realization in which all valid sentences of the theory are satisfied and a possible realization of the theory is an entity of the appropriate set theoretical structure. . . . It is my opinion that this notion of model is the fundamental one for the empirical sciences as well as mathematics. To assert this is not to deny a place for variant uses of the word "model" by empirical scientists, as for example when a physicist talks about a physical model.{21}I have not included "theory" as a separate component of a cognitive matrix because I take it that theories are a set of statements which include definitions, laws, and sometimes interpretative models. Let me turn next to the strange term which I included as part of a cognitive matrix,namely, "paragon." A dictionary defines "paragon" as "a model of excellence or perfection: pattern; a paragon of beauty; a paragon of eloquence; a paragon of virtue." I would like to enter another example to illustrate the meaning of paragon as a model of excellence or perfection, namely, Newton's Principia for a long time was a paragon of science; or Lavoisier's Chemistry was a paragon of the science of chemistry. The advantages of being able to point to a certain man like Jesus Christ or Ghandi and say that he is a paragon of virtue is that this usually satisfies a rough first approximation to what is meant by a virtuous man. It enables the inquirer to zero in on the model and ultimately to spell out those characteristics that are essential in a virtuous man. Our conception of a virtuous man changes from time to time. The paragon model however, enables people of a particular culture and time to try to imitate the particular paragon even in the absence of an explicit set of characteristics that such a paragon implies. I would like to suggest that similarly, in science a scientist at a particular time might not be able to spell out all the rules of the right way of doing science (i. e., physics, chemistry, etc.). He might, however, and often does, point to a paragon of his science. He might cite Newton's Principia or Lavoisier's Chemistry suggesting that this is the right way of doing science. Because scientists can agree on such paragons during a particular time, this makes possible a coherent scientific tradition. The paradox of a coherent scientific tradition is thus resolved. Although scientists do not have a complete set of rules which direct their research, nevertheless, they can agree on the paragon examples of the way to do science. Furthermore, there should be no confusion between "paradigm" and "paragon" for paradigms are clear-cut examples of terms such as "compound" or "mixture" and paragons are such things as classical scientific papers and textbooks. Paradigms are the sorts of illustrations of concepts students acquire who study such paragons of science as Newton's Principia, which for a time defines science. There are obvious difficulties with citing a paragon in answer to such questions as "what is science?", "what is virtue?" In each case there are many ambiguities that lurk behind such examples. Unless some characteristics are cited, a novice might easily pick on aspects of a paragon that are not essential. This is primarily why a novice scientist is trained in a laboratory under the supervision of a senior scientist.{22} The fact that scientists may be trained in the absence of an explicit set of essential characteristics of the paragon should not be taken as an excuse for not attempting to identify such characteristics. Under the model of science described in Chapter III of this work this is one of the main objectives of the so-called normal scientific research. Likewise, I would like to suggest that one of the main tasks of a philosopher of science is to spell out those essential characteristics of science and explicate those notions of science that are implicit in such paragons. Prior to the appearance of paragons scientists can, at times, be guided by certain principles which are for a time assumed to be important. Rather than look for "paradigms" in Kuhn's sense which transmits no one clear meaning, a historian of science might do better to search out what principles have guided certain types of research. Look, for example, at the important role that the principle of a balanced chemical equation (i. e., the weight of chemicals before the experiment must equal the weight of chemicals after the experiment) had in guiding research in chemistry. Initially it implicitly guided some of the research of phlogiston chemists. When such research led to the discovery of certain anomalies which resulted in the overthrow of phlogiston theory, the principle survived the revolution and was then openly adopted by Lavoisier and later chemists as an important guide in research. There were and still are many such guiding principles in the history of science and I suspect that they night be easier to find than "paradigms" in Kuhn's sense. I have included categories as an additional component of a cognitive matrix because I want to stress the point that an important part of some scientific discoveries is the creation of a new category or a new pigeon hole, for the classification of the types of basic phenomena that scientists believe to be part of nature. When Lavoisier discovered a new type of element heretofore assured to be just air, he was forced to introduce the term "oxygen" in order to inform future scientists about its existence as a new type of phenomena distinct in kind from others. Scientific specialties have as the objects for study in their domains certain types of phenomena. These types of phenomena are identified by the set of categories developed by scientists in a field of specialty. If we were to combine all the categories of all our sciences believed to be not empty, they would form a conceptual web designed to capture all the discreet aspects of nature. With scientific revolutions usually come changes in our categories. With the coming of Lavoisier's chemistry the category of "phlogiston" was assumed to be empty and was thus, dropped from our chemical terminology. Concerning the components of meta-science, I would first of all like to make clear that they are also subject to modification and change, but change is a much rarer phenomenon here than in the cognitive matrix. There are good reasons for this. I have discussed at great length in Chapter I section (D) the first of the components of meta-science, namely, criteria of choice for an adequate scientific theory. I believe that such criteria as are given in T5 do not necessarily change with change in a scientific specialty for they pertain to the very essence of science per se. Since our ideal of an adequate scientific theory, if it changes at all, changes very slowly these criteria also change slowly and always for very good reasons. Deductive logic, like mathematics, is an eidetic science. The development of deductive logic like the development of mathematical theories proceeds independently of any scientific theory. Such development particularly in mathematical theories must precede the development of certain types of scientific theories. Without mathematics, science would not be the successful discipline that it is. At times a scientist must make innovations in mathematical systems because he needs such a system for the statement of his theory. But at such times the scientist takes on the role of the mathematician and this part of his work will be judged by the canons appropriate to mathematical cogency and proof. Thus, new mathematical theories can come into existence specifically in answer to the need that some scientist has in the formulation of his theory. Such occurrences are rare. What is more often the case is that mathematicians have already developed many more mathematical theories than scientists have found applications for. Very nearly the same is true of logical systems. Logicians develop logical theories for which philosophers and scientists have yet to find practical applications or even interpretations of their variables. I am specifically referring here to the recent developments in the so called many-valued logics. Some of these n-valued logics, for example, the three valued logic, seem to be well suited for application to quantum mechanics. A system of logic or mathematics does not change, however, with change in scientific theories. What does happen is that with new scientific theories other systems of logic than the traditional two-valued logic might be found to be more appropriate. Similarly, new applications might be found for mathematical systems with the developments in scientific theories. My proposal no longer has the aura of mystery as was true with the term "paradigm". All of the components of a cognitive matrix are terms that have an accepted usage and some philosophers and scientists have already made some progress in further explicating these terms. The cognitive matrix underlying the research and problem-solving of a scientific community can and very often does have ontological commitments as to the kind of entities that make up the universe. Instead of speaking of paradigms as determining reality, I would like to speak of the ontological presuppositions of a cognitive matrix. Likewise, another ambiguity can be resolved by drawing a distinction between a narrow cognitive matrix and basic cognitive matrix. If you recall, Kuhn sometimes speaks of paradigms as basic theories which are of universal scope -- such as Newtonian dynamics -- and sometimes he speaks of paradigms in terms of narrower theories or specialties such as Newton's optical theory or Lavoisier's chemical theory. Even though it is true to say that all fields of science presuppose some aspects of a cognitive matrix, nevertheless, it can be said that some C. M. are basic and others are of limited scope. In summary, let me turn to the problem of evaluating my rational reconstruction of Kuhn's terminology in the SSR. In the first place my reconstruction is in the spirit of SSR for as I have shown above, my terminology is capable of facilitating the resolution of the two paradoxes. Secondly, my reconstruction contains terms that are less ambiguous. Above all, I have not introduced any radically new meaning. On the contrary, my reconstruction has laid a bridge between Kuhn's work and the work of many philosophers in philosophy of science. Above all, I have sketched a framework in terms of which one can bring together diverse work that is done in the field of philosophy of science. Rather than pick one term like "theory," "model," or "paradigm," etc. and try to do justice in terms of it alone to the whole field of science, as so many have done, I have constructed a conceptual scheme which is broad enough to incorporate most of the known aspects of science. Much work remains to be done, but it is hoped that some paths have been charted through the dense forest of science.
Table of Contents -- Go to Chapter 4
Notes {1} H. V. Stopes-Roe in a review of the book proposes the following reading of the term "paradigm". "I would suggest, in fact, that if a reader wishes to bring out the real content of what Kuhn is saying, he may find it advantageous to try substituting 'basic theory' for every occurrence of 'paradigm' in the book . . ." Review of SSR in the British Journal for the Philosophy of Science (1964-65), p. 159. [Back]
{2} W. Stegmuller, "Towards a Rational Reconstruction of Kant's Metaphysics of Experience," manuscript. Criteria for an adequate rational reconstruction are presented on p. 2 [Back]
{3} See particularly Chapter V of SSR, "The Priority of Paradigms," pp. 43-51. [Back]
{4} Ibid., pp. 44-45. [Back]
{5} Scheffler, Science and Subjectivity, p. 17. [Back]
{6} SSR, p. 10. [Back]
{7} "As a result, the reception of a new paradigm often necessitates a redefinition of the corresponding science. Some old problems may be relegated to another science or declared entirely 'unscientific.' . . . And as the problems change, so, often, does the standard that distinguishes a real scientific solution from a mere metaphysical speculation, word game, or mathematical play." (SSR, p. 102) [Back]
{8} 0f paradigms Kuhn states: "These I take to be universally recognized scientific achievements that for a time provide model problems and solutions to a community of practitioners." (SSR, p. x) [Back]
{9} SSR, p. 43. [Back]
{10} For a complete list of the various senses of the term "paradigm" e see Chapter I section (A) of this work. [Back]
{11} Webster's Third New International Dictionary of the English Language Unabridged, ed. P. B. Gove (Springfield, Mass.: G. & C. Merriam Co., 1966). [Back]
{12} Carney and Scheer, Fundamentals of Logic (Macmillan Company), p. 70. [Back]
{13} Ibid., p. 69. [Back]
{14} Ludwig Wittgenstein, Philosophical Investigations, trans. G. E. M. Anscombe (New York, 1953), pp. 31-36. [Back]
{15} SSR, pp. 50-51. [Back]
{16} "Cognitive matrix" was the term suggested by Professor Kuhn in one of our discussions. He also proposed at that time the following components of such a cognitive matrix: laws, definitions, paradigms, and models. Any additional components as well as the division of a conceptual scheme into the cognitive matrix and meta-science are my innovations. [Back]
{17} An excellent treatment of the kinds and various roles of definitions in science is provided by Peter Achinstein's Concepts of Science, Chapter I and II. [Back]
{18} For an analysis of the concept of law and of its role in scientific explanation and prediction see Carl Hempel Aspects of Scientific Explanation and Other Essays in the Philosophy of Science (New York: The Free Press, 1964), in particular Chapter IV, "Scientific Explanation"; also Nelson Goodman, Fact, Fiction and Forecast (Indianapolis: Bobbs-Merrill Co., Inc., 1965), Chapter I, "The Problem of Law." [Back]
{19} See in particular Mary Hesse, Models and Analogies in Science, (University of Notre Dare Press, 1966). [Back]
{20} Pierre Duhem, The Aim and Structure of Physical Theory (Atheneum, New York, 1962), pp. 96-97. [Back]
{21} E. Nagel, P. Suppes, and A. Tarski (eds.), Logic, Methodology and Philosophy of Science, Proceedings of 1960 International Congress (California: Stanford University Press, 1962), p. 252. For a further discussion of analogies in science see Peter Achinstein's Concepts of Science, Chapter VII "Analogies and Models" and Chapter VIII "On a Semantical Theory of Models." [Back]
{22} See H. A. Krebs, "The Making of a Scientist," Agricultural Science Review, VI, 2 (1968). Krebs discusses the importance of studying under great scientists if one is to be capable of making a great scientific discovery. [Back]
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